Geosystem Engineering, 7(1), 12-20 (March 2004)

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*Corresponding Author: Yilong QinE-mail: yilongqin@mail.igcas.ac.cnAddress: Institute of Geology & Geophysics ChineseAcademy Sciences Qijiahuozi, Chaoyang District, Beijing,China, 100029

A Robust and Accurate Traveltime Calculation from Frequency-domain Two-way Wave-equation Modeling Algorithm

Yilong Qin1*, Seungwon Ko2, Changsoo Shin2, Zhongjie Zhang1, Youngtak Seo2, Uk Han3 and Yun Chen1

1Institute of Geology and Geophysics, Chinese Academy of Sciences, Qijiahuozi, Beijing 100029, China2Seoul National University, School of Civil, Urban and Geosystem Engineering, Seoul, 151-742, Korea

3Department of Environment Science, Korea Military Academy, Seoul, 139-799, Korea.

ABSTRACT : We improve the accuracy and stability oftraveltime calculation method using frequency-domainmodeling algorithm. We perform a parameter analysis toobtain the optimum combination of frequency and damp-ing factor and thus improve the accuracy of traveltime.Then we obtain the empirical formula for our numericalalgorithm. Lastly, we propose the adaptive frequency andthe adaptive damping factor for an inhomogeneous modelto eliminate the distortion in the traveltime contour. Two-dimensional numerical examples verify that the proposedalgorithm gives a much smaller traveltime error and abetter traveltime contour for the complex model. Com-pared to the other two methods, this algorithm computestraveltime that is close to a directly transmitted wave. Wedemonstrated our algorithm on 2D IFP Marmousi models,and the numerical results show that our algorithm is afaster traveltime calculation method of a directly transmit-ted wave for imaging the subsurface and transmissiontomography.

Key words : traveltime calculation, frequency-domain model-ing, parameter analysis

INTRODUCTION

A robust and accurate traveltime calculation is of criti-cal importance for transmission tomography, refractiontomography, earthquake seismology, and prestack Kirch-hoff migration. To this end, geophyicists have developeda variety of traveltime calculation techniques. Most of thetechniques can be divided into four categories: (1) ray-

tracing method; (2) Eikonal solver (Kim, 2002; Mo andHarris, 2002; Afnimar and Koketsu, 2000; Alkhalifah andFomel, 2001) (3) Shortest-path algorithm (Cheng andHouse, 1996; Cao and Greenhalgh, 1993; Fischer andLees, 1993); and (4) traveltime calculation from a waveequation modeling algorithm (Shin et al., 2002, 2003a,2003b). These methods have their own characteristics.Compared with other methods, the traveltime calculationusing the wave-equation modeling algorithm has its ownadvantages. Its (1) more suitable for a computation ofmulti-shot traveltime used in Kirchhoff migration; (2) canbe modified to calculate the most-energetic traveltime(Shin et al., 2003a, 2003b; Nichols, 1996); (3) can beeasily extended to elastic media or anisotropic media; and(4) can simultaneously calculate traveltime and amplitude.

The traveltime calculation using the frequency-domainmodeling algorithm was originally proposed by Shin etal. (2003a). They applied a complex frequency (the realpart is the frequency, and the imaginary part is the damp-ing factor) into the frequency-domain wave-equation andthen approximated the damped wavefield in the depth byusing the Dirac delta function. Thus, they transformed thedifficult traveltime picking problems into an easier maxi-mum-arrival picking problem. For this algorithm, thechoice of frequency and damping factor is critical foraccuracy of the traveltime since different combinations ofthe frequency and the damping factor give different trav-eltimes. Conventionally, the frequency and the dampingfactor are determined from dispersion analysis (Shin etal., 2003a). However, the dispersion analysis has difficultyin giving the optimum combination of frequency anddamping factor since a different dispersion error limitderives a different frequency and damping factor. Essen-tially, the dispersion analysis only considers the dispersionerror and neglects the assumption of high-frequencyapproximation. Actually, for the traveltime calculation fromthe frequency-domain modeling algorithm, accurate travel-time depends on not only dispersion error but also thehigh-frequency approximation. Only a very small grid sizecan satisfy both of the requirements. Unfortunately,because of the limitations of computer memory and speed,the number of model grids cannot be too large. When thegrid size is fixed, there is a trade-off between the disper-

A Robust and Accurate Traveltime Calculation from Frequency-domain Two-way Wave-equation Modeling Algorithm 13

sion and assumption of high-frequency approximation,that is, the small dispersion requires a low frequency, butthe high-frequency approximation requires a high fre-quency. Therefore, to obtain the best traveltime, we mustfind the optimum combination of the frequency and thedamping factor. In addition, the traveltime contour com-puted by the basic algorithm is distorted for heterogeneousmedia.

In this paper, we improve the accuracy and stability ofthe traveltime calculation from the frequency-domain wave-equation modeling algorithm. The accuracy is improvedby using parameter analysis to obtain the optimum com-bination of the frequency and the damping factor. Thestability is improved by using an adaptive frequency andan adaptive damping factor to eliminate the distortedtraveltime contour in an inhomogeneous medium.

We begin by reviewing the numerical solution of thefrequency-domain two-way wave equation. We review thesimple technique that computes the traveltime. Next, wepropose the parameter analysis to obtain the optimumcombination of the frequency and the damping factor andthe adaptive complex frequency to eliminate the distortedtraveltime contour. Finally, we give the numerical exam-ples for the IFP Marmousi model and compare our travel-time with the most-energetic and Straight-Ray-Technique(SRT) traveltime. We also generate Kirchhoff-migratedimages by using our adaptive traveltime for the 2DMarmousi model.

BASIC THEORY

Damping factorWe assumed that a seismic signal observed at a receiver

in depth can be approximated by a series of weightedspikes (Fig. 1a). The weighted series of spike can beexpressed as

(1)

where the An and tn are the amplitude and the nth digi-tized time (countered from the first-arrival event), respec-tively. In general, if we multiply equation (1) by a strongdamping factor, we can suppress all the events followingthe first arrival, as shown in Fig. 1b, and thus approxi-mate the solution as

(2)

where A1 and t1 are the amplitude and traveltime of thefirst arrival. By suppressing all the wave events follow-ing the first arrival, we transform the difficult traveltimepicking problems into an easier maximum-arrival pickingproblem.

Two-way frequency-domain modelingWe calculate traveltime by using a two-way frequency-

domain wave equation. The scalar wave equation for ahomogeneous isotropic medium in the frequency domainis

(3)

where the u is the pressure field, ω is the angular fre-quency, and ν is the velocity. The frequency-domain,finite-difference formulation for the scalar wave equationcan be written as

(4)

where M, C, and K are the n� n (n is the number of nodalpoints) mass, damping, and stiffness matrices, respectively;f and u are the n� n source and data vectors, respectively;m is the model vector comprised of the impedance andvelocity at each nodal coordinate, and . For sim-plicity, we express the above equation as

(5)

where the complex impedance matrix S is given by

(6)

u t( ) Anδ t tn–( )n∑=

u∗ t( ) u t( )eα t–

A1eα t–≅ δ t t1–( )=

u2∇ ω2

ν2------u+ 0=

K m( ) iωC m( ) ω2M m( )–+[ ] u m ω,( ) f ω( )=

i 1–=

S m ω,( )u m ω,( ) f ω( )=

S K iωC ω2M–+=

Fig. 1. Synthetic seismograms for a 2-D earth model. (a) theseismic signal can be approximated by a series ofweighted, and (b) delta-like wavefield obtained by intro-ducing a strong damping factor α = 100

14 Yilong Qin et al.

In principle, we could calculate the inverse of S to obtainthe wavefield , where we recognize G to bethe Green function. In practice, we do not explicitly calcu-late but rather decompose S into the product of a lowertriangular matrix and an upper triangular matrix. We thencalculate the wavefield u by forward and backward sub-stitution. Matrices associated with 2-D finite-differencemeshes are amenable to the modern sparse matrix technique.

Traveltime calculation from the frequency-domainwavefield

We calculate the traveltime from the wavefield, obtainedby inserting a complex angular frequency into the frequency-domain wave equation, in the forward modeling. A com-plex angular frequency is expressed as

(7)

where ω is the real angular frequency and α is the sup-pression factor that is commonly used to prevent wrap-around effects inherent in frequency-domain solutions. Byvirtue of the shifting theorem of Fourier-domain trans-forms, the factor α suppresses the time-domain solutionby e-αt. In conventional frequency-domain modeling, wesynthesized our time-domain solutions from the Fouriercomponent ω*, where α is a constant and ω varies, andmultiplied the final time-domain results by the inverse ofthe damping factor, eαt.

By using complex frequencies, we can reduce the generalmultiple event response to a single event. The resultingsingle event can correspond to the first arrival. Accordingto equations (1) and (2), the time-domain wavefield obtainedby the two-way wave-equation with complex angular fre-quency can be approximated as

(8)

where , u is the wavefield, isthe traveltime from the source to a depth point in the sub-surface, is the amplitude at the depth point in thesubsurface, and δ is the Dirac delta function. In the fre-quency-domain, the equation above can be written as

(9)

Differentiating the above equation with respect to gives

(10)

From the equation above, we compute the traveltime bydividing du/dω by iu. The derivative of wavefield u withrespect to ω can be calculated using forward and backwardsubstitution. For example, taking the partial derivative ofequation (5) with respect to complex frequency ω yields

(11)

After arranging the equation, we obtain

(12)

where the virtual source vector is associated with theperturbation of the complex frequency and is given by

(13)

Equation (12) has the same form as equation (5), whereu and f are replaced by and , respectively. Sincethe f in equation (5) is constant, the derivative of f becomeszero. The vector is a new source used to compute thederivative of the wavefield . Once we factorize thematrix S and obtain the wavefield u in the frequencydomain, the computation of the derivative wavefield onlyrequires one more forward and backward substitution.

IMPROVEMENTS ON ACCURACY AND STABILITY

Improvement on the accuracy of traveltimeFor the traveltime calculation from the frequency-domain

modeling algorithm, an accurate traveltime requires a

u S 1– f Gf≡=

ω * ω iω+=

u x z t, ,( ) A x z t, ,( )δ t τ x z t, ,( )–( )=

A x z,( ) A x z,( )eα t–

= τ x z t, ,( )

A x z t, ,( )

u x z ω, ,( ) A x z,( )eiωτ x z,( )–

=

du x z ω, ,( )dω

-------------------------- iτ– x z,( )A x z,( )eiωτ x z,( )–≈

iτ– x z,( )u x z ω, ,( )=

S m ω,( )∂u m ω,( )∂ω-----------------------

∂S m ω,( )∂ω

-----------------------u m ω,( )+ 0=

S∂u∂ω------- f=

f

f∂u∂ω-------u 2ωm iC–( )u=–=

∂u ∂ω⁄ f

f∂u ∂ω⁄

Fig. 2. Analytic traveltimes (solid lines) and numerical trav-eltimes (dotted lines) computed by using a different fre-quency and damping factor (a) f = 1 Hz, α = 55; (b)f = 10 Hz, α = 140. The velocity is 2.0 km/s.

A Robust and Accurate Traveltime Calculation from Frequency-domain Two-way Wave-equation Modeling Algorithm 15

proper selection of the frequency and the damping factor,since different combinations of the frequency and thedamping factor give different traveltimes, as shown inFig. 2. A large frequency can approximate the assumptionof high-frequency, but cause large numerical dispersion.Similarly, a large damping factor can strongly damp allthe wavefields except the first-arrival event, but require afine grid to minimize the dispersion error, which conse-quently increases computational cost. A small dampingfactor will introduce error in picking the traveltime, becausethe damped wavefield is approximated by the Dirac deltafunction. Therefore, in order to obtain an accurate travel-time, we need to consider not only the dispersion error butalso the assumption of high-frequency approximation. Ifwe use a very small grid size, we can satisfy both thedispersion and the high-frequency assumption. Unfortu-nately, for a frequency-domain wave-equation modelingalgorithm, the solution of the sparse matrix requires a largememory and a high amount of CPU time. Therefore, wecannot use a very small grid size. For a given grid size,there is a trade-off between the dispersion and the high-frequency assumption. Our problem was how to choose theoptimum combination of frequency and damping factorfor a given grid size.

Conventionally, the frequency and damping factor aredetermined from the dispersion analysis (Shin et al.,2003a):

(14)

where G is the number of grid points per wavelengthdetermined from dispersion curves for a given dispersionerror limit; ω* is the optimum complex frequency; Varg isthe average velocity of a given model; Vmin is the minimumvelocity for one given model, and ∆ is the grid interval.

Since the dispersion analysis determines the optimumcomplex frequency in terms of only the dispersion error,it is difficult to achieve the optimum complex frequency.Moreover, the dispersion analysis varies with the detailednumerical algorithm. Therefore, we propose the parameteranalysis in order to get an optimum combination of fre-quency and damping factor

To illustrate how we use the parameter analysis to obtainthe optimum frequency and damping factor in solving thetwo-way frequency-domain wave equation by the finite-difference method, we first examine a 2-D homo-geneoushalf-space model with a 1151� 376 grid set, the grid sizeof 8 m, and a constant velocity of 2 km/s. The source is

placed at the 600th grid at the surface. Then, we computethe traveltime error for this homogeneous model as afunction of the frequency and damping factor. Fig. 3ashows the total absolute error between the computed trav-eltime and the analytic traveltime. In Fig. 3a, the sum ofthe traveltime errors is 387.56 s and the correspondingfrequency and damping factor as 10 Hz and 55, respectively.Thus, the average error for this model becomes 0.0008955 s.The traveltime computed using the optimum complex fre-quency is shown in Fig. 4a. Additionally, the error betweenthe numerical traveltime computed with the optimumcomplex frequency and the analytic traveltime is shownin Fig. 4b. From Fig. 4b, we note that the computed trav-

ω * 2πVmin

G∆------------------= i

2πVavg

G∆------------------+

Fig. 3. The absolute error of traveltime with respect to frequencyand damping factor for homogeneous models: (a) v = 2km/s and (b) v = 8 km/s. The grid interval is 8 m. Thenumber of grids is 1151� 376.

Table 1. Comparison of the error of our method with that of the method used by Shin et al. (2003a). The average error of our method ismuch smaller than that of Shin et al. (2003a), although the size of our model is 8 times larger than that used in Shin et al.(2003a).

Grid size Velocity Number of grids Maximum error Average error

Shins method 5m 1.5km/s 401*201 0.0055s 0.0025s

Our method 8m 2km/s 1151*376 0.004s 0.00089s

16 Yilong Qin et al.

eltime are compatible with the analytic traveltime. In Fig.4b, all of the errors are less than 0.004 s, and the averageerror is 0.0008955 s. In Table 1, we compare the error ofour algorithm with that of the basic algorithm suggestedby Shin et al. (2003a). From Table 1, we can note thatthe average error of our algorithm is much smaller than thatof the basic algorithm of Shin et al. (2003a), although thesize of our model is eight times larger than the modelused in Shin et al. (2003a).

Improvement on the stabilityUsing parameter analysis, we can get the optimum com-

bination of frequency and damping factor for a homoge-neous media with a velocity of 2 km/s. In order toestimate how the optimum frequency and damping factor

varies with the velocity, we apply the parameter analysisto another homogenous model with a different velocity.Fig. 3b is the result of parameter analysis for one modelwith a constant velocity of 8 km/s. From Fig. 3b, we canknow that the optimum frequency and damping factor is40 Hz and 220, respectively, when the velocity is 8 km/s.The comparison of the optimum frequency and dampingfactor for the two different models is shown in Table 2.From Table 2, we note that there is a linear relationshipbetween velocity and optimum frequency or optimumdamping factor. Therefore, we obtain the following empir-ical formula for our numerical method

(15)

where the Gf = 25, Gα = 25, and ∆ is the grid size.Equation (15) is accurate for homogeneous media. For

heterogeneous media, we usually replace the velocity termin equation (15) with a minimum velocity and averagevelocity as

(16)

where Vmin and Vavg is the minimum velocity and the aver-

ω * 2πVGf∆----------= i

2πVGα∆-----------+

ω * 2πVmin

Gf∆------------------= i

2πVavg

Gα∆------------------+

Fig. 4. (a) Analytic (solid line) and numerical traveltimes com-puted by using the optimum frequency and dampingfactor (dotted line) for the homogeneous model whosevelocity is 2 km/s; (b) The corresponding errorsbetween the analytic traveltimes and the numerical trav-eltimes.

Table 2. Optimum complex frequency for different velocities inhomogeneous media.

Velocity Grid sizeOptimum Frequency

Optimum Damping Factor

2 km/s 8 m 10 Hz 55

4 km/s 8 m 20 Hz 110

8 km/s 8 m 40 Hz 220

Fig. 5. Marmousi model overlaid by traveltime contour cal-culated by using (a) the method of Shin et al. (2003a)and (b) the adaptive frequency and the adaptive dampingfactor.

A Robust and Accurate Traveltime Calculation from Frequency-domain Two-way Wave-equation Modeling Algorithm 17

age velocity, respectively, in the inhomogeneous model.The traveltime for the Marmousi model computed withequation (16) is shown in Fig. 5a. In Fig. 5a, we observethat the traveltime contour is obviously distorted. Shin etal. (2003a) speculated that the distorted contours of trav-eltimes resulting from multiple events with nearly thesame amplitude as or larger amplitude than that of the first-arrival event.

To overcome the problem, we propose the followingadaptive optimum frequency and the damping factor forheterogeneous media

(17)

where the Gf = 25, Gα = 28.54, ∆ is the grid size, i and jis the vertical coordinate and horizontal coordinate,respectively. From equation (17), we can note that theparameter G changes according to frequency and dampingfactor. The traveltime for the Marmousi model, computedusing equation (17), is shown in Fig. 5b. From Fig. 5b, wecan see that the distortion observed in Fig. 5a disappears.

COMPARISON WITH OTHER TRAVELTIMES

Having successfully demonstrated that our algorithm hasboth higher accuracy and better stability, we proceeded tocompare the travel times obtained by our method with themost-energetic traveltime obtained with the method usedby Shin et al. (2003b) and the traveltime obtained by the(Lim et al., 2002). In Fig. 6a, we display the traveltimecontours computed by our method and the most-energetictraveltime. In Fig. 6a, we note that the traveltime computedby our method shows good agreement with the most-energetic traveltime. From the traveltime contour far awayfrom source in Fig. 6a, we note that the traveltime com-puted by our algorithm is comparable to the transmittedwaves rather than the first arrival. We also compared ourtraveltime with the traveltime generated by the SRT in Fig.6b. The traveltime obtained by the SRT approximatelydescribes the direct wave. From Fig. 6b, we note that ourtraveltime contour has good agreement with that of theSRT. To verify further that our traveltime is very close tothe transmitted wave, rather than the head wave, wedevised a simple model with three layers. The velocity ofeach layer from the top to the lower is 1500, 2000 and2800 m/s. In Fig. 7a, we overlap the resulting traveltimecontours on the velocity model. In Fig. 7a, we observethat there is head wave in the zone far away from thesource, and the traveltime contour in the zone far awayfrom the source obviously corresponds to the transmittedwave. In Figs. 7b and 7c, we also compute the transmitted-wave traveltime using a one-way wave equation and thefirst-arrival traveltime using the finite-difference methodof Vidale (1988).

Next, we check whether or not the traveltime obtained by

our method yielded good migration images. Figs. 8a and8b show the prestack Kirchhoff migration images usingonly the traveltime computed with our method and themost-energetic traveltime obtained by using the method ofShin et al. (2003b). From Fig. 8a, we note that the migra-tion image obtained by our traveltime is better than theresult computed by the most-energetic traveltime. We alsoadded the most-energetic amplitude to the correspondingtraveltime to get the Kirchhoff migration images, as shownin Figs. 9a and 9b. In Fig. 9, we note that the imagescomputed by our traveltime give better resolved faults andreservoir and that the results are compatible with theimages computed by the most-energetic traveltime andamplitude.

CONCLUSIONS

By calculating traveltime error as the function of fre-quency and damping factor for different velocities whenthe grid size is fixed, we obtain the optimum frequencyand the optimum damping factor for different velocities. We

ω *i j,( ) 2πV i j,( )

Gf∆----------------------= i

2πV i j,( )Gα∆

----------------------+

Fig. 6. (a) Traveltime contours calculated by our method (dottedline) and the most energetic traveltime contour (solidline) obtained with the method used by Shin et al.(2003b) for the Marmousi model, superimposed on theamplitude image of the most energetic. The velocitieschange from 1500 m/s at the top of the model to 5500m/s at the bottom of the model; and (b) the comparisonbetween our traveltime (dotted line) and the SRT trav-eltime (solid line) for the Marmousi model.

18 Yilong Qin et al.

then derive an accurate empirical formula for our numericalalgorithm. The accuracy of traveltime is much improvedby using the optimum frequency and the optimum dampingfactor derived from the parameter analysis. We appliedthe adaptive frequency and the adaptive damping factor toeliminate the distorted traveltime contour for heterogeneousmedia. Compared with the most-energetic traveltime andthe SRT traveltime, our algorithm calculates the traveltimethat is comparable to the directly transmitted wave ratherthan the head wave.

Fig. 7. (a) Traveltime computed by our method for a three-layermodel, (b) the transmitted-wave traveltime computedusing a one-way wave equation. (c) the first-arrival trav-eltime computed by using Vidales method (1988). Thevelocity of each layer from the top to the lower is 1500,2000 and 2800 m/s, respectively

Fig. 8. Prestack Kirchhoff migration images for the Marmousimodel using (a) traveltime obtained by our algorithmand (b) the most-energetic traveltime obtained by Shinet al. (2003b)

Fig. 9. Prestack Kirchhoff migration images generated by using(a) the traveltime obtained by our algorithm and (b) themost energetic traveltime obtained by Shin et al.(2003b) for the Marmousi model. For two migrationimages, we use the same amplitudes.

A Robust and Accurate Traveltime Calculation from Frequency-domain Two-way Wave-equation Modeling Algorithm 19

ACKNOWLEGEMENTS

This study is sponsored by the Chinese State NaturalScience Foundation (49825108), the Chinese Academy ofSciences (KZCX2-109 and KZ951-B1-407-02), and theKorea Foundation for Advanced Studies. This work wasalso financially supported by the National LaboratoryProject of the Ministry of Science and Technology andthe Brain Korea 21 project of the Ministry of Education.

REFERENCES

Afnimar and Koketsu, K., 2000, Finite difference traveltimecalculation for head waves traveling along an irregularinterface: Geophysical Journal International, Vol. 143, p.729-734

Alkhalifah, T. and Fomel, S., 2001, Implementing the fastmarching eikonal solver: spherical versus Cartesian coor-dinates: Geophysical Prospecting, Vol. 49, p. 165-178.

Cao, S. and Greenhalgh, S. A., 1993, Calculation of the seis-mic first-break time field and its ray path distributionusing a minimum traveltime tree algorithm: GeophysicalJournal International, Vol. 114, p. 593-600.

Cheng, N. and House, L., 1996, Minimum traveltime calcula-tion in 3-D graph theory: Geophysics, Vol. 61, p. 1895-1898.

Fischer, R. and Lees, J. M., 1993, Shortest path ray tracingwith sparse graphs: Geophysics, Vol. 58, p. 987-996.

Kim, S., 2002, 3-D eikonal solvers: First-arrival traveltimes:Geophysics, Vol. 67, p. 1225-1231.

Lim, H. Y., Min, D. -J., Shin C., and Yang, D., 2002,Prestack depth migration using Straight Ray Technique(SRT): Journal of Seismic Exploration, Vol. 11, p. 271-281.

Mo, L. W. and Harris, J. M., 2002, Finite-difference calcula-tion of direct-arrival traveltimes using the eikonal equa-tion: Geophysics, Vol. 67, p. 1270-1274.

Nichols, D. E., 1996, Maximum energy traveltimes calcu-lated in the seismic frequency band: Geophysics, Vol. 61,p. 253263.

Shin, C., Ko, S., Kim, W., Min, D. J., Yang, D. and MarfurtK. J., 2003a, Traveltime calculations from frequency-domain downward-continuation algorithms. Geophysics,Vol. 68 p. 1380-1388

Shin, C., Ko, S. W., Marfurt, K. J. and Yang, D., 2003b,Wave equation calculation of most energetic traveltimesand amplitudes for Kirchhoff prestack migration: Geo-physics, Vol. 68, p. 2040-2042.

Shin, C., Min, D. J., Marfurt, K. J., Lim, H.Y., Yang D.,Cha, Y., Ko, S., Ha, T. and Hong, S., 2002, Traveltimeand amplitude calculations using the damped wave solu-tion: Geophysics, Vol. 67, p. 1637-1647.

Vidale, J., 1988, Finite-difference calculation of travel times:Bulletin of the Seismological Society of America, Vol. 78,p. 2062-2076.

20 Yilong Qin et al.

Zhang Zhongjie Qin Yilong Chen Yun Changsoo Shin

Seungwon Ko Young Tak Seo Han Uk

Zhang Zhongjie received Ph.D (1991) in Geophysics fromJilin University. He worked in the Standford University as avisiting scholar and visiting professor in 1996 and 2000,respectively. Presently, he is a research professor in the Insti-tute of Geology & Geophysics, Chinese Academy of Sci-ences (CAS). His current research interest includes seismicanisotropic modeling, tomography, crust/mantle structure andgeodynamics.(E-mail: zhangzj@mail.iggcas.ac.cn)

Qin Yilong received a BS (1997), an MS (2000) in explora-tion geophysics from Daqing Petroleum Institute, and Ph.D(2003) in seismology from the Institute of Geology & Geo-physics, Chinese Academy of Sciences (CAS). Currently, heis a research assistant in the Institute of Geology & Geophys-ics, CAS, and his current research interest includes traveltimecalculation in anisotropic media, Kirchhoff migration andtraveltime tomography.(E-mail: yilongqin@mail.igcas.ac.kr)

Chen Yun received a BS (1997) in Geophysics from JilinUniversity and MS (2004) in exploration geophysics fromChina University of Geosciences, Beijing. From 1997 topresent, he works in the Institute of Geology & Geophysics,Chinese Academy of Sciences (CAS). His current researchinterest includes seismic tomography, wavefield analysis andseismic anisotropy.(E-mail: yunchen@mail.iggcas.ac.cn)

Changsoo Shin received a PhD (1988) in geophysics fromthe University of Tulsa. After working at the Korea Instituteof Geology, Mining, and Materials from 1990 to 1996, he

became an associate professor of geophysics at SeoulNational University. He has led the national research labora-tory of seismic inversion and imaging of Seoul National Uni-versity since June 2000. His interests are the numericalmodeling of wave propagation, full waveform inversion, andgeophysical imaging. (E-mail: css@model.snu.ac.kr)

Seungwon Ko received his BS(1994), MS(1996), Ph.D(2001)from Hanyang University. He was a visiting scholar in AGL(Allied Geophysical Laboratory) in Houston after his Ph.Dand is currently working in technical department ofKNOC(Korea National Oil Corporation). His main researcharea is seismic data processing and especially, scalar and vec-tor PSDM (Prestack Depth Migration) and seismic inversion.(E-mail: ko@gpl.snu.ac.kr)

Young Tak Seo is a student in Ph.D course in Civil, Urbanand Geosystem Engineering at Seoul National University. Heholds BS degree in Mineral and Resources Engineering fromSemyung University and MS degree in Geophysical Prospect-ing from Seoul National University.(E-mail: geoneer@empal.com)

Han Uk received a BS(1970), an MS(1974) in Astronomyfrom Seoul National University, and MS(1979)/Ph.D(1984) inThermal Processes and Tectonophysics from the University ofUtah, SLC, USA. Currently, he is a professor in the Dept. ofEnvironmental Sci., Korea Military Academy.(E-mail: jigugong@chollian.net)